The underlying mechanism in the charged case would be no different from the
normal case of neutral particles and walls. To see why, think for a minute
about why particles bounce off of neutral surfaces to begin with. If you
look very closely at a neutral atom striking a neutral surface, you'll see
that the recoil comes from the electron shell of the atom repelling from
the electron shells of the surface's atoms. So in fact, the pressure from
the neutral case results from the electromagnetic force just as in the
charged case. I mention this because, from your question, it appears you
think of the pressure resulting from repulsion of like charges to be
somehow different in essence from what normally occurs in a container.
That said, there IS a difference between the two cases. In the charged
case, the electromagnetic force between the particles and the walls is
obviously larger than in the neutral case. Because it now takes much more
energy for a particle to approach the walls, the effective volume of the
container is decreased. The ideal gas law (PV=nkT) therefore tells us that
the pressure will be greater (for the same amount of gas at the same
temperature) in the charged case than in the neutral case.